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The paper investigates the solvability of a boundary value problem in the control of an oscillatory process described by control in partial derivatives of the first order. It has been established that there are an infinite set of controls, as solutions to the system of nonlinear Fredholm integral equations of the first kind, each of which transfers the controlled process from the initial state to the final specified state in a specified time. Sufficient conditions for the existence of a nonlinear optimization solution are found.
Let L4 be a 4-dimensional Lorentzian space with the sign (−,,,). The aim of this study is to investigate the other missing algebraic forms of the constraint manifolds of 2C and 3C spatial open chains in L4. For this purpose, firstly, we obtain the structure equations of a spatial open chain using the equations of open chains of the Lorentz plane and Lorentz sphere. After then, using these structure equations, we search the algebraic forms of the constraint manifolds of 2C and 3C spatial open chains in Lorentzian 3-space with respect to the causal characters of the first link and the axis of ro ...Более
Let a normalized analytic function be given on the open unit disk. In this paper, we define and consider some familiar subsets of analytic functions associated with sine functions in the region of unit disk on the complex plane. For these classes, we aim to find the upper bounds of the modules of the Hankel determinants obtained from the coefficients of the functions belonging to some classes defined by subordination.
Keyword: analytic functions; coefficient estimates; convex function; hankel determinant; sine function; starlike functions; subordination